points represented by the table lie on a line. Find the slope of the line. x & -9 & -5 & -1 & 3 y & -2 & 0 & 2 & 4 10. x & -1 & 2 & 5 & 8 y & -6 & -6 & -6 & -6 11. x & 0 & 0 & 0 & 0 y & -4 & 0 & 4 & 8 12. x & -4 & -3 & -2 & -1 y & 2 & -5 & -12 & -19

## Step 1: Identify the table with points that lie on a line<br />### We need to determine which of the given tables represents points that lie on a straight line. This can be done by checking if there is a constant rate of change (slope) between the x and y values.<br /><br />## Step 2: Calculate the slope for each table<br /><br />### **First Table:**<br />- Points: (-9, -2), (-5, 0), (-1, 2), (3, 4)<br />- Calculate the slope \( m \) using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \).<br />- For points (-9, -2) and (-5, 0): <br /> \[<br /> m = \frac{0 - (-2)}{-5 - (-9)} = \frac{2}{4} = \frac{1}{2}<br /> \]<br />- For points (-5, 0) and (-1, 2):<br /> \[<br /> m = \frac{2 - 0}{-1 - (-5)} = \frac{2}{4} = \frac{1}{2}<br /> \]<br />- For points (-1, 2) and (3, 4):<br /> \[<br /> m = \frac{4 - 2}{3 - (-1)} = \frac{2}{4} = \frac{1}{2}<br /> \]<br />- The slope is consistent at \(\frac{1}{2}\).<br /><br />### **Second Table:**<br />- Points: (-1, -6), (2, -6), (5, -6), (8, -6)<br />- All y-values are the same, indicating a horizontal line.<br />- Slope \( m = 0 \).<br /><br />### **Third Table:**<br />- Points: (0, -4), (0, 0), (0, 4), (0, 8)<br />- All x-values are the same, indicating a vertical line.<br />- Slope is undefined.<br /><br />### **Fourth Table:**<br />- Points: (-4, 2), (-3, -5), (-2, -12), (-1, -19)<br />- Calculate the slope:<br />- For points (-4, 2) and (-3, -5):<br /> \[<br /> m = \frac{-5 - 2}{-3 - (-4)} = \frac{-7}{1} = -7<br /> \]<br />- For points (-3, -5) and (-2, -12):<br /> \[<br /> m = \frac{-12 - (-5)}{-2 - (-3)} = \frac{-7}{1} = -7<br /> \]<br />- For points (-2, -12) and (-1, -19):<br /> \[<br /> m = \frac{-19 - (-12)}{-1 - (-2)} = \frac{-7}{1} = -7<br /> \]<br />- The slope is consistent at \(-7\).<br /><br />## Step 3: Determine which table has a consistent slope<br />### The first table has a consistent slope of \(\frac{1}{2}\), indicating that the points lie on a straight line.